91Ó°ÊÓ

The subpart $\left(a\right)$a sample of $Pd-103$after $34$days with a half-life of $17$days fits subpart$\left(2\right)$.

(part a)$Pd-103$has a half-life of $17$day in a sample.

Half-life: A radioisotope's half-life is the time it takes for half of a sample to decay.

After $34$days, calculate the half-lives of $Pd-103$.

$Pd-103\stackrel{1halflife}{→}17daysPd-103\stackrel{2halflives}{→}34days$

$Pd-103$has two half-lives after $34$days.

As a result, subpart $\left(a\right)$a $Pd-103$sample with a half-life of $17$days after $34$days fits subpart $\left(2\right)$.

The subpart $\left(b\right)$a sample of $C-11$with a half-life of $20$minutes after $20$ minutes corresponds to subpart $\left(1\right)$.

(part b) $C-11$having a $20$-minute half-life.

Calculate the elapsed half-life for $C-11$after localid="1652188675800" $20min$.

localid="1652188652936" $\mathrm{C}-11\stackrel{1\text{half-life}}{âŸ\P }20\min$

After $20min$, $C-11$has one half-life.

As a result, subpart $\left(b\right)$a sample of $C-11$with a half-life of $20$minutes after $20$minutes corresponds to subpart .

The subpart $\left(c\right)$, a sample of $At-211$with a half-life of role="math" localid="1652189164176" $7h$after role="math" localid="1652189173917" $21h$, corresponds to subpart$\left(3\right)$.

(part c) $At-211$sample with a $7h$half-life.

After using $21h$, calculate the half-lives for $At-211$.

$At-211\stackrel{1\text{half-life}}{âŸ\P }7hAt-211\stackrel{\text{2half-lives}}{âŸ\P }14hAt-211\stackrel{\text{3half-lives}}{âŸ\P }21hAt-211$

After $21h$, $At-211$has three half-lives.

As a result, subpart $\left(b\right)$a sample of $C-11$with a half-life of $20$minutes after $20$minutes corresponds to subpart$\left(1\right)$.